Add the papaya, onion, sugar and vinegar to a medium saucepan. Bring to a simmer and cook, uncovered, until the papaya is soft and the liquid has reduced slightly, 10 to 15 minutes. Remove from the heat and cool completely over a bowl of crushed ice.
Stir in the garlic, olive oil, ginger, cilantro, thyme and lime juice. Season to taste with salt and pepper and serve.